Bank data ($8001-$9FFF, odd)

R6 and R7 will ignore the top two bits, as the MMC3 has only 6 PRG ROM address lines. Some romhacks rely on an 8-bit extension of R6/7 for oversized PRG-ROM, but this is deliberately not supported by many emulators. See iNES Mapper 004 below.

R0 and R1 ignore the bottom bit, as the value written still counts banks in 1KB units but odd numbered banks can't be selected.

Though these bits are functional on the MMC3, their main purpose is to write-protect save RAM during power-off. Many emulators choose not to implement them as part of iNES Mapper 4 to avoid an incompatibility with the MMC6.

IRQ latch ($C000-$DFFE, even)

7 bit 0
---- ----
DDDD DDDD
|||| ||||
++++-++++- IRQ latch value

This register specifies the IRQ counter reload value. When the IRQ counter is zero (or a reload is requested through $C001), this value will be copied to the IRQ counter at the NEXT rising edge of the PPU address, presumably at PPU cycle 260 of the current scanline.

IRQ reload ($C001-$DFFF, odd)

7 bit 0
---- ----
xxxx xxxx

Writing any value to this register reloads the MMC3 IRQ counter at the NEXT rising edge of the PPU address, presumably at PPU cycle 260 of the current scanline.

IRQ disable ($E000-$FFFE, even)

7 bit 0
---- ----
xxxx xxxx

Writing any value to this register will disable MMC3 interrupts AND acknowledge any pending interrupts.

IRQ enable ($E001-$FFFF, odd)

7 bit 0
---- ----
xxxx xxxx

Writing any value to this register will enable MMC3 interrupts.

Hardware

The MMC3 most commonly exists in a 44-pin TQFP package.
Three revisions are known to exist - MMC3A, MMC3B, and MMC3C. No major behavioral differences are known, except for the IRQ counter.

IRQ Specifics

The MMC3 scanline counter is based entirely on PPU A12, triggered on rising edges (after the line remains low for two rising edges of M2).

The counter is based on the following trick: whenever rendering is turned on in the PPU, it fetches nametable and BG pattern tiles from dots 0-255 and 320-340 of a scanline and fetches sprite patterns from dots 256-319, even if no sprites are visible.
Because of this, if BG uses the left pattern table ($0000), and if sprites always use the right pattern table ($1000), A12 will remain low during all nametable and BG pattern fetches, and high during all sprite pattern fetches, causing it to oscillate exactly one time per scanline and 241 times per frame. It may oscillate more if the program uses registers $2006 and $2007 to access PPU $1000-$1FFF during vblank, but this is rare because very few games have MMC3 and CHR RAM (two on TQROM and three on TGROM among NES games, and a couple more Famicom-only games). The scanline counter will also work when the BG uses the right pattern table ($1000) and the sprites use the left pattern table ($0000), but this is less common. The MMC3 IRQ has two revisions that work slightly different [1].

Counter operation:

When the IRQ is clocked (PPU A12 0->1), the counter value is checked - if zero or the reload flag is true, it's reloaded with the IRQ latched value at $C000; otherwise, it decrements.

If the IRQ counter is zero and IRQs are enabled ($E001), an IRQ is triggered. The "alternate revision" checks the IRQ counter transition 1->0, whether from decrementing or reloading.

Regarding PPU A12:

When using 8x8 sprites, if the BG uses $0000, and the sprites use $1000, the IRQ counter should decrement on PPU cycle 260, right after the visible part of the target scanline has ended.

When using 8x8 sprites, if the BG uses $1000, and the sprites use $0000, the IRQ counter should decrement on PPU cycle 324 of the previous scanline (as in, right before the target scanline is about to be drawn).

When using 8x16 sprites PPU A12 must be explicitly tracked. The exact time and number of times the counter is clocked will depend on the specific set of sprites present on every scanline. Specific combinations of sprites could cause the counter to decrement up to four times, or the IRQ to be delayed or early by some multiple of 8 pixels. If there are fewer than 8 sprites on a scanline, the PPU makes a dummy fetch to tile $FF ($1FF0-$1FFF) for each leftover sprite. Thus if a game uses 8x16 sprites with its background and sprites from PPU $0000, then the MMC3 ends up counting each scanline that doesn't use all eight sprites.

Important points:

The scanline counter cannot be stopped. It will continue to decrement and reload as long as PPU A12 on the PPU bus toggles.

There is no direct access to the counter! The best that can be done is update the reload value and immediately request a reload.

Writing to $E000 will only prevent the MMC3 from generating IRQs - the counter will continue to run.

Writing to $E001 will simply allow the MMC3 to generate IRQs - the counter remains unaffected.

Writing to $C001 will cause the counter to be cleared, and set reload flag to true. It will be reloaded on the NEXT rising edge of the PPU A12.

Writing to $C000 does not immediately affect the value within the counter - this value is only used when the counter is reloaded, whether from reaching 0 or from writing to $C001.

The exact number of scanlines between IRQs is N+1, where N is the value written to $C000. 1 (Sharp MMC3B, MMC3C) or 2 (MMC3A, Non-Sharp MMC3B) to 256 scanlines are supported.

The counter will not work properly unless different pattern tables for background and sprite data are in use. The standard configuration is to use PPU $0000-$0FFF for background tiles and $1000-$1FFF for sprite tiles, whether 8x8 or 8x16.

The counter is clocked on each rising edge of PPU A12, no matter what caused it, so it is possible to (intentionally or not) clock the counter by writing to $2006, regardless of whether PPU is/is not rendering.

There's a slight discrepancy with what happens when $C000 is set to $00, and so far, two behaviors are known to exist:

All MMC3A's and non-Sharp MMC3B's will generate only a single IRQ when $C000 is $00. This is because this version of the MMC3 generates IRQs when the scanline counter is decremented to 0. In addition, writing to $C001 with $C000 still at $00 will result in another single IRQ being generated. In the community, this is known as the "alternate" or "old" behavior.

All MMC3C's and Sharp MMC3B's will generate an IRQ on each scanline while $C000 is $00. This is because this version of the MMC3 generates IRQs when the scanline counter is equal to 0. In the community, this is known as the "normal" or "new" behavior.

Acclaim's MC-ACC chip is their own variant of the MMC3, that they used for their own boards (for industrial money-saving purposes). It comes in a standard 600 mil 40-pin DIP package. It is not known if it has SRAM support. The only known difference is that the scanline counter triggers on falling edges instead of rising edges.

iNES Mapper 004 and MMC6

Since the new header is not yet well adopted among emulators or ROM sets, an approach that supports both MMC3 and MMC6 may be desired when an NES 2.0 header is not used.

The MMC6 has a smaller PRG-RAM, and a different register scheme for write protecting it.

Because write protection is generally only used to guard against corruption during power off, many implementations of iNES Mapper 004 simply omit the write protection. Leaving PRG-RAM always write-enabled removes most of the incompatibility between MMC3 and MMC6, and is sufficient to support the popular MMC6 games StarTropics and StarTropics II. These games do not rely on the smaller PRG-RAM size of the MMC6, so the larger 8k RAM addressed by the MMC3 is not a problem.

The less well known game Low G Man is problematic. It used an MMC3 board with no PRG-RAM. Because of a bug in its music code, it relies on open-bus behaviour in the RAM's address range to function correctly. The game does use the MMC3 mechanism to disable RAM, so it may function on an MMC3 board with PRG-RAM, but implementing the MMC3 RAM disable may conflict with the effort to support MMC6 games. Alternatively, NES 2.0 could be used to specify a PRG-RAM size of 0, or the problem can be resolved by patching the Low G Man ROM to work around the conflict: patch.

Some romhacks attempt to increase the available PRG-ROM size beyond the MMC3's hard 512k limit (e.g. Translation of Final Fantasy III). Full 8-bit banking registers could theoretically support up to 2048K PRG-ROM, but very few emulators implement this extension.

Variants

Board wiring variants

The TKSROM and TLSROM boards, assigned to INES Mapper 118, connect the upper bank select line directly to VRAM A10, allowing more flexible control over nametable mirroring.

The TQROM board, assigned to INES Mapper 119, uses both CHR ROM and CHR RAM simultaneously, using the 2nd-highest CHR bank select line to choose between them (on a per-bank basis).

Nintendo made at least two MMC3-based multicart mappers: mappers 37 and 47.

MMC3-like chips variants

The DxROM board, assigned to iNES Mapper 206 has a custom mapper developed by Namco before the MMC3 existed. It has no IRQ or mirroring control.
Tengen used it for some of their games under the name MIMIC-1.
It exists both in a 400 mil 28-pin Shrink-DIP (found in licensed DxROM boards) and in a larger 600 mil 28-pin DIP (found in unlicensed Tengen cartridges).

The Namco 108/MIMIC-1 does the basic ROM banking exactly like the MMC3, but it only implements the low 3 bits of $8000 and the low 6 bits of $8001. Compared to the MMC3, it lacks mirroring control, SRAM support and an IRQ counter. The TEROM and TFROM boards have been developed with backward compability with DxROM in mind, featuring solder pads to have hardwired H/V mirroring instead of MMC3 controlled mirroring, and allow the hardware to disable IRQs.

Nintendo MMC3 chip variants

IRQ behavior when reload is set to 0 differs among different MMC3 chips.
MMC3 chips with the "new behavior" generate an IRQ every scanline.
(These include at least MMC3B chips bearing a bold S before the date code.)
MMC3 chips with the "old behavior" cease to generate IRQs.
(These include MMC3B chips lacking the S and having a date code of the form nnnnPKnnn, and an MMC3A 8940EP chip.)
Some games have been manufactured with both versions, and during the transition, relying on old or new behavior might at first have been one of the things that caused Nintendo lot check to reject a program.
A few later games developed after Nintendo had run out of the old chips, such as Star Trek: 25th Anniversary, are reported to rely on the new behavior (source: Nestopia 1.30 changelog).

There's an anecdotal report that Felix the Cat needs MMC3A, but it's necessarily not related to the IRQ behavior since the game works correctly in emulators that only implement the MMC3C behavior.